Theory of local distortion in ErO6 cluster: Spontaneous symmetry reduction in lanthanoid octahedrons

Molecular orbital calculations for an ${\mathrm{ErO}}_6$ cluster predicted a stable ${\mathrm{C}}_{\text{4v}}$ pseudo-octahedron with an Er displacement of ∼0.1 Å from the center of the octahedron with an $\mathrm{Er}–\mathrm{O}$ bond length of 2.27 Å. In this particular configuration, the hybridization balance of $\mathrm{O}\text{\hspace{0.05em}2p–}\mathrm{Er}\text{\hspace{0.05em}6s}$ with $\mathrm{O}\text{\hspace{0.05em}2p–}\mathrm{Er}\text{\hspace{0.05em}5d}$ minimizes electron transfer from the O anion to the Er cation, thereby strengthening the $\mathrm{Er}–\mathrm{O}$ ionic bond. Excessive $\mathrm{O}\text{\hspace{0.05em}2p–}\mathrm{Er}\text{\hspace{0.05em}5d}$ hybridization due to π-bond formation is found in the shorter $\mathrm{Er}–\mathrm{O}$ bond range, while insufficient hybridization caused by a weak σ-bond is obtained in the longer $\mathrm{Er}–\mathrm{O}$ bond range. Though spontaneous reduction of symmetry has also been confirmed in other ${\mathrm{LO}}_6$ $(\mathrm{L}{=}^{65}\mathrm{Tb}{–}^{71}\mathrm{Lu})$ systems, the stablest pseudo-octahedron is obtained for ${\mathrm{ErO}}_6.$